1. Consider the language L described by the regular expression: ( 0 U 1(01^*0)^*1 )^*
   1. List all strings in L of length five or shorter.

2. Draw a DFA or NFA that recognizes L. You dont need to use the construction we discussed, just make sure whatever automaton you come up with recognizes L.

3. Suppose the strings in L are taken to be integers represented in base-2 (possibly with leading 0s). Describe the set of integers that are in L. (By describe, I mean a simple characterization like All the prime numbers.)

2. Draw the state diagram for a simple DFA with three states that recognizes the strings over {a, b} that contain an even number of as or end in a b. Hint: The start state is an accept state and one of the other two states is the other accept state.

3. Use the construction in Sipser to convert your DFA from Question 2 into an equivalent regular expression. You must draw several GNFAs starting with the initial one (Recall: The initial GNFA has a special form.)